In general, local h-refinement is more difficult in IGA (Isogeometric analysis) compared to FEM (Finite element method) because IGA shape function constructed using tensor products. To address this issue, S-IGA (S-version of Isogeometric Analysis) has been proposed. S-IGA uses of the concepts of S-FEM (s-version of Finite element method) to IGA, overlaying a local IGA model (representing local features) onto a global IGA model (representing global features). However, when the global IGA model has a complex geometry, overlaying local IGA model becomes challenging because their free surfaces may not perfectly coincide. In this presentation, we propose that the geometry of local IGA model be defined in the natural coordinates of global IGA model. Hence, the geometry of the local IGA model is defined by the interpolation functions for the global IGA model. The geometry of free surfaces of the global and local IGA model completely coincides. Through numerical examples, we demonstrate the convergence of the solution. Furthermore, we adopt singular patch to accurately reproduce the so-called square-root-R stress singularity. The numerical examples demonstrate that the proposed method effectively and accurately performs fracture mechanics analysis for complex shaped structures.